My answer to a question on Quora: Why isn’t math presented as a language at school?

As usual, an answer is rather frustrating: because mathematics is taught on the cheap, and by teachers who have not been properly educated themselves (and they should not be blamed for that).

Mathematics has many aspects, and most of them remain unknown to many learners — and teachers — of mathematics. Of all metaphorical descriptions of mathematics, one of my favorites is

Mathematics is a language of contracts with Nature which Nature accepts as binding.

Within mathematics, people talk about “language of set theory”, or “language of categories”, or “language of algebraic topology”, or “language of schemes” — the list could be continued almost indefinitely.

To teach mathematics as a language means, first of all, giving students a chance to see that the same problem can formulated, say, in the language of algebra and in the language of geometry, and see the advantages and drawbacks of the two languages, and translate from one language to another, and combine both in a solution. This can be done — but this will be more expensive. Most school systems in the world cannot afford that; richer countries can afford that, but there is no political will to do that. Indeed, what for?

There is another aspect of mathematics which is almost never mentioned: in humans, mathematics is done by the subconscious, and mathematical languages are to certain degree languages of communication with the subconscious. I wrote about that elsewhere. If you want me to continue discussion of that fascinating facet of mathematics, please leave a comment to this post.